Determinism No-Go Under Perfect Self-Containment: { Diagonal-Capable Records Forbid Total-Effective Record Determinism in Theories with Genuine Record-Divergent Choice}

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-13
DOI
https://doi.org/10.5281/zenodo.22733145
Primary Topic
Computability, Logic, AI Algorithms
Type
preprint
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preprint

Determinism No-Go Under Perfect Self-Containment: { Diagonal-Capable Records Forbid Total-Effective Record Determinism in Theories with Genuine Record-Divergent Choice}

Nova Spivack
Zenodo (CERN European Organization for Nuclear Research)
Computability, Logic, AI Algorithms
preprint

Determinism No-Go Under Perfect Self-Containment: { Diagonal-Capable Records Forbid Total-Effective Record Determinism in Theories with Genuine Record-Divergent Choice}

Nova Spivack
preprint en

Abstract

We prove a determinism no-go theorem for closed physical theories with macroscopic records. Using the machine-checked NEMS classification spine and the machine-checked diagonal barrier, we show that in any perfectly self-contained (PSC) framework that is both (i) diagonal-capable at the record level (i.e. it can encode universal computation and halting as record-truth), and (ii) admits genuine record-divergent choice (multiple admissible continuations disagreeing on records), there is no total effective deterministic law that maps past records to unique future records on the diagonal-capable fragment. Formally, any purported total computable "record determinism" function would induce a total computable decider for diagonal-capable record-truth, contradicting the diagonal barrier (proved via reduction to Mathlib's halting undecidability theorem). The proof is kernel-verified in Lean 4 with zero custom axioms. This establishes a Gödel/Turing-class limitation on deterministic closure: if a theory is PSC and admits record-divergent choice, then any determinism compatible with diagonal-capable records must be non-total-effective (or must retreat to record-categoricity / triviality). Given physical universal computation and halting-expressibility at the record level, determinism is ruled out, not assumed. This overview presents the core NEMS theorem engine and selected applications; stronger domain-specific derivation and ontological synthesis claims belong to separate release surfaces with their own premise bundles and formal artifacts.

Zenodo (CERN European Organization for Nuclear Research)
Peace, Justice and strong institutions
Computability, Logic, AI Algorithms
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